This invention relates to providing a system for improved hot liquid drinking systems. More particularly, this invention relates to providing a cover for a beverage container which assists shifting the temperature of at least one portion of consumable liquid toward room temperature prior to delivery from the drinking vessel to a consumer. More particularly, this invention relates to providing a cover for a drinking vessel which promotes thermal exchange between at least one portion of consumable liquid and the surrounding environment prior to delivery from the beverage container to a consumer. While drinking a hot beverage such as coffee, tea, or hot chocolate, a consumer may experience physical discomfort due to sipping a beverage which is too hot. Alternatively, while drinking a cold beverage such as frozen coffee, smoothie, or milk shake, a consumer may experience physical discomfort due to sipping a beverage which is too cold. Therefore, a need exists for a system which assists shifting the temperature of a portion of consumable liquid towards room temperature prior to delivery to the mouth of the consumer, in order to prevent burning or freezing of the mouth of the consumer.